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Syllabus and Exam Weightage

Below is the CBSE Class 11 Maths Chapter wise weightage. Extramarks provides the best learning material which is kept along the lines of CBSE Class 11 Maths Chapter Wise Weightage. Students can prepare for all the chapters according to the CBSE Chapter Wise Weightage Class 12 for securing Extramarks in exams. Below are the chapters included in Class 12. There CBSE Weightage is given.
Chapter 1 – Relations and Functions
Chapter 2 – Inverse Trigonometric Functions
Chapter 3 – Matrices
Chapter 4 – Determinants
Chapter 5 – Continuity and Differentiability
Chapter 6 – Application of Derivatives
Chapter 7 – Integrals
Chapter 8 – Application of Integrals
Chapter 9 – Differential Equations
Chapter 10 – Vector Algebra
Chapter 11 – Three Dimensional Geometry
Chapter 12 – Linear Programming
Chapter 13 – Probability
Below is a very brief description of Linear Programming which is an important topic as far as CBSE Class Weightage is concerned.
Linear programming (also known as statistical optimization) is a special case of mathematical programming.

More generally, linear programming is a methodology for maximizing a continuous objective function, subject to limitations of linear consistency and linear inequalities. The feasible area is a convex polytope, a structure described as the intersection of many finite half-spaces, each of which is defined by a linear inequality. The objective function is described on this polyhedron by a real-valued affine (linear) function. A linear programming algorithm finds a point in the polytope where, if such a point exists, this function has the smallest (or greater) value. Linear programming can apply to different fields of study. It is commonly used in mathematics, and in finance, economics, and for some engineering problems to a lesser extent. Industries use linear programming models include shipping, electricity, communications, and manufacturing. It has been proved useful in modelling various types of preparation, routing, arranging, selection, and design problems.

In 1939 the Soviet economist Leonid Kantorovich provided a linear programming formulation of a problem which is similar to the general linear programming problem, who also suggested a method for solving it. It is a method he built during World War II to schedule spending and returns to reduce army costs and increase enemy casualties. In the USSR the study of Kantorovich was originally ignored. About the same date as Dutch-American theorist Kantorovich T. C. Koopmans proposed fundamental questions of the economy as sequential programs. Early on, Kantorovich and Koopmans shared the Nobel Prize in Economics in 1975. Frank Lauren Hitchcock also proposed transport problems as linear programs in 1941 and provided a very similar solution to the later simplex method. Hitchcock died in 1957 and is not posthumously awarded the Nobel prize.

George B. Dantzig developed general linear programming techniques separately between 1946–1947 to be used for preparation issues within the US Air Force. Also in 1947, Dantzig introduced the simplex method which in most cases effectively tackled the issue of linear programming for the first time. Once Dantzig arranged a meeting to explore his simplex approach with John von Neumann, Neumann instantly conjectured the principle of duality after discovering that the problem he had been focusing on in-game theory was equivalent[4]. Dantzig presented systematic proof in an unfinished January 5, 1948 article called ""A Theorem on Linear Inequalities."" In the years after the war, it was used by many companies throughout their regular preparation.

The initial definition of Dantzig was finding the best distribution of 70 workers to 70 jobs. The computing power needed to check all permutations for selecting the best assignment is vast; the number of possible configurations in the observable universe exceeds the number of particles. Nonetheless, seeking the optimum solution requires only a moment, by introducing the question as a linear system and using the simplex algorithm. The linear programming principle greatly reduces the number of possible solutions that have to be verified.
 In 1984 when Narendra Karmarkar introduced a new method of interior design to solve linear programming problems. Extramarks provides the best learning material for Class 12. Students can prepare from all the topics that are included in the syllabi of Class 12. The chapters are in the lines of CBSE Chapter-Wise Weightage Class 12.

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